Extremes in incomplete samples from moving averages of random variables from the domain of attraction of the Gumbel distribution

Abstract

We are interested in further extremal properties of the moving average process defined from an i.i.d. noise sequence with common distribution function belonging to the maximum domain of attraction of the Gumbel extreme value distribution and satisfying additionally two specific conditions. In particular, we consider the limiting behavior of a sequence of random vectors consisted of maxima in complete and incomplete samples from this class of moving averages. The point process approach is used to derive the corresponding results.